Procedure for generating operational ballistic capture transfer using a computer implemented process

ABSTRACT

A method generates an operational ballistic capture transfer for an object emanating substantially at earth or earth orbit to arrive at the moon or moon orbit using a computer implemented process. The method includes the steps of entering parameters including velocity magnitude V E , flight path angle γ E , and implementing a forward targeting process by varying the velocity magnitude V E , and the flight path angle γ E  for convergence of target variables at the moon. The target variables include radial distance, r M , and inclination i M . The method also includes the step of iterating the forward targeting process until sufficient convergence to obtain the operational ballistic capture transfer from the earth or the earth orbit to the moon or the moon orbit.

RELATED APPLICATIONS

This patent application is a continuation of U.S. application Ser. No.09/277,743, filed Mar. 29, 1999, now U.S. Pat. No. 6,278,946 which is acontinuation of International application Ser. No. PCT/US98/01924, filedFeb. 4, 1998, which claims priority from U.S. provisional patentapplication serial No. 60/036,864, filed Feb. 4, 1997, U.S. provisionalpatent application serial No. 60/041,465, filed Mar. 25, 1997, U.S.provisional patent application serial No. 60/044,318, filed Apr. 24,1997, U.S. provisional patent application serial No. 60/048,244, filedJun. 2, 1997, all to inventor Edward A. Belbruno, and all of which areincorporated herein by reference, including all references citedtherein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates in general to methods for space travel, and inparticular, to methods for an object, such as a satellite, space craft,and the like, to be placed in lunar orbit around the moon, and/or orbitaround other planets including earth.

2. Background of the Related Art

The study of motion of objects, including celestial objects, originated,in part, with Newtonian mechanics. During the eighteenth and nineteenthcenturies, Newtonian mechanics, using a law of motion described byacceleration provided an orderly and useful framework to solve most ofthe celestial mechanical problems of interest for that time. In order tospecify the initial state of a Newtonian system, the velocities andpositions of each particle must be specified.

However, in the mid-nineteenth century, Hamilton recast the formulationof dynamical systems by introducing the so-called Hamiltonian function,H, which represents the total energy of the system expressed in terms ofthe position and momentum, which is a first-order differential equationdescription. This first order aspect of the Hamiltonian, whichrepresents a universal formalism for modeling dynamical systems inphysics, implies a determinism for classical systems, as well as a linkto quantum mechanics.

By the early 1900s, Poincare understood that the classical Newtonianthree-body problem gave rise to a complicated set of dynamics that wasvery sensitive to dependence on initial conditions, which today isreferred to as “chaos theory.” The origin of chaotic motion can betraced back to classical (Hamiltonian) mechanics which is the foundationof (modern) classical physics. In particular, it was nonintegrableHamiltonian mechanics and the associated nonlinear problems which posedboth the dilemma and ultimately the insight into the occurrence ofrandomness and unpredictability in apparently completely deterministicsystems.

The advent of the computer provided the tools which were hithertolacking to earlier researchers, such as Poincare, and which relegatedthe nonintegrable Hamiltonian mechanics from the mainstream of physicsresearch. With the development of computational methodology combinedwith deep intuitive insights, the early 1960s gave rise to theformulation of the KAM theorem, named after A. N. Kolmogorov, V. l.Arnold, and J. Moser, that provided the conditions for randomness andunpredictability for nearly nonintegrable Hamiltonian systems.

Within the framework of current thinking, almost synonymous with certainclasses of nonlinear problems is the so-called chaotic behavior. Chaosis not just simply disorder, but rather an order without periodicity. Aninteresting and revealing aspect of chaotic behavior is that it canappear random when the generating algorithms are finite, as described bythe so-called logistic equations.

Chaotic motion is important for astrophysical (orbital) problems inparticular, simply because very often within generally chaotic domains,patterns of ordered motion can be interspersed with chaotic activity atsmaller scales. Because of the scale characteristics, the key element isto achieve sufficiently high resolving power in the numericalcomputation in order to describe precisely the quantitative behaviorthat can reveal certain types of chaotic activity. Such precision isrequired because instead of the much more familiar spatial or temporalperiodicity, a type of scale invariance manifests itself. This scaleinvariance, discovered by Feigenbaum for one-dimensional mappings,provided for the possibility of analyzing renormalization groupconsiderations within chaotic transitions.

Insights into stochastic mechanics have also been derived from relateddevelopments in nonlinear analysis, such as the relationship betweennonlinear dynamics and modern ergodic theory. For example, if timeaverages along a trajectory on an energy surface are equal to theensemble averages over the entire energy surface, a system is said to beergodic on its energy surface. In the case of classical systems,randomness is closely related to ergodicity. When characterizingattractors in dissipative systems, similarities to ergodic behavior areencountered.

An example of a system's inherent randomness is the work of E. N. Lorenzon thermal convection, which demonstrated that completely deterministicsystems of three ordinary differential equations underwent irregularfluctuations. Such bounded, nonperiodic solutions which are unstable canintroduce turbulence, and hence the appellation “chaos,” which connotesthe apparent random motion of some mappings. One test that can be usedto distinguish chaos from true randomness is through invocation ofalgorithmic complexity; a random sequence of zeros and ones can only bereproduced by copying the entire sequence, i.e., periodicity is of noassistance.

The Hamiltonian formulation seeks to describe motion in terms offirst-order equations of motion. The usefulness of the Hamiltonianviewpoint lies in providing a framework for the theoretical extensionsinto many physical models, foremost among which is celestial mechanics.Hamiltonian equations hold for both special and general relativity.Furthermore, within classical mechanics it forms the basis for furtherdevelopment, such as the familiar Hamilton-Jacobi method and, of evengreater extension, the basis for perturbation methods. This latteraspect of Hamiltonian theory will provide a starting point for theanalytical discussions to follow in this brief outline.

As already mentioned, the Hamiltonian formulation basically seeks todescribe motion in terms of first-order equations of motion. Generally,the motion of an integrable Hamilton system with N degrees of freedom isperiodic and confined to the N-torus as shown in FIG. 1. FIG. 1 depictsan integrable system with two degrees of freedom on a torus, and aclosed orbit of a trajectory. The KAM tori are concentric versions ofthe single torus. Hamiltonian systems for which N=1 are all integrable,while the vast majority of systems with N greater than or equal to 2become nonintegrable.

An integral of motion which makes it possible to reduce the order of aset of equations, is called the first integral. To integrate a set ofdifferential equations of the order 2N, that same number of integralsare generally required, except in the case of the Hamiltonian equationsof motion, where N integrals are sufficient. This also can be expressedin terms of the Liouville theorem, which states that any region of phasespace must remain constant under any (integrable) Hamiltonian formalism.The phase space region can change its shape, but not its phase spacevolume. Therefore, for any conservative dynamical system, such asplanetary motion or pendula that does not have an attracting point, thephase space must remain constant.

Another outcome of the Hamiltonian formulation, which started out as aformulation for regular motion, is the implication of the existence ofirregular and chaotic trajectories. Poincare realized thatnonintegrable, classical, three-body systems could lead to chaotictrajectories. Chaotic behavior is due neither to a large number ofdegrees of freedom nor to any initial numerical imprecision. Chaoticbehavior arises from a nonlinearity in the Hamiltonian equations withinitially close trajectories that separate exponentially fast into abounded region of phase space. Since initial conditions can only bemeasured with a finite accuracy and the errors propagate at anexponential rate, the long range behavior of these systems cannot bepredicted.

The effects of perturbations in establishing regions of nonintegrabilitycan be described for a weak perturbation using the KAM theorem. The KAMtheorem, originally stated by Kolmogorov, and rigorously proven byArnold and Moser, analyzed perturbative solutions to the classicalmany-body problem. The KAM theorem states that provided the perturbationis small, the perturbation is confined to an N-torus except for anegligible set of initial conditions which may lead to a wanderingmotion on the energy surface. This wandering motion is chaotic, implyinga great sensitivity to initial conditions.

The N-tori, in this case, are known as KAM surfaces. When observed asplane sections they are often called KAM curves as illustrated in FIG.2. These surfaces and curves may be slightly distorted (perturbed). Thatis, for a sufficiently small conservative Hamiltonian perturbation, mostof the nonresonant invariant tori will not vanish, but will undergo aslight deformation, such that in the perturbed system phase space thereare also invariant tori, filled by phase curves, which are conditionallyperiodic.

FIG. 2 illustrates a set of KAM invariant tori on the surface of whichlie as elliptic integrable solutions. The nonintegrable solutions,irregular paths, which are hyperbolic in nature lie in between theinvariant tori in so-called resonant zones, which are also sometimesreferred to as stochastic zones.

The KAM results were extended through the results of J. Mather. KAMtheory treats motions and related orbits that are very close to beingwell behaved and stable. Since KAM theory is basically a perturbationanalysis, by its very nature the perturbation constant must be verysmall. Strong departures from the original operator through theperturbation parameter will invalidate the use of the originaleigenfunctions used to generate the set of perturbed eigenfunctions.Mather's work analyzes unstable motions which are far from being wellbehaved. The perturbation can be relatively strong, and entirely neweigenfunctions (solutions) can be generated.

The practical importance of Mather's work for planetary orbit, escape,and capture is that the dynamics are applicable to those regions inphase space (i.e., Mather regions) associated with three- and four-bodyproblems. Mather proved that for chaotic regions in lower (two)dimensions for any conservative Hamiltonian System, there exists orremains elliptical orbits which are unstable. In terms of NEO(near-Earth object) issues, KAM and Mather regions are important fordescribing both the orbital motions of comets, as well as for planningfuel conserving ballistic (flyby, rendezvous, and interception)trajectories to comets and other NEOs. The above discussion is a summaryof the article by John L. Remo, entitled “NEO Orbits and NonlinearDynamics: A Brief Overview and Interpretations,” 822 Annals of the NewYork Academy of Sciences 176-194 (1997), incorporated herein byreference, including the references cited therein.

Since the first lunar missions in the 1960s, the moon has been theobject of interest of both scientific research and potential commercialdevelopment. During the 1980s, several lunar missions were launched bynational space agencies. Interest in the moon is increasing with theadvent of the multi-national space station making it possible to stagelunar missions from low earth orbit. However, continued interest in themoon and the feasibility of a lunar base will depend, in part, on theability to schedule frequent and economical lunar missions.

A typical lunar mission comprises the following steps. Initially, aspacecraft is launched from earth or low earth orbit with sufficientimpulse per unit mass, or change in velocity, to place the spacecraftinto an earth-to-moon orbit. Generally, this orbit is a substantiallyelliptic earth-relative orbit having an apogee selected to nearly matchthe radius of the moon's earth-relative orbit.

As the spacecraft approaches the moon, a change in velocity is providedto transfer the spacecraft from the earth-to-moon orbit to amoon-relative orbit. An additional change in velocity may then beprovided to transfer the spacecraft from the moon-relative orbit to themoon's surface if a moon landing is planned. When a return trip to theearth is desired, another change in velocity is provided which issufficient to insert the spacecraft into a moon-to-earth orbit, forexample, an orbit similar to the earth-to-moon orbit. Finally, as thespacecraft approaches the earth, a change in velocity is required totransfer the spacecraft from the moon-to-earth orbit to a low earthorbit or an earth return trajectory.

FIG. 3 is an illustration of an orbital system in accordance with aconventional lunar mission in a non-rotating coordinate system whereinthe X-axis 10 and Y-axis 12 lay in the plane defined by the moon'searth-relative orbit 36, and the Z-axis 18 is normal thereto. In atypical lunar mission, a spacecraft is launched from earth 16 or lowearth orbit 20, not necessarily circular, and provided with sufficientvelocity to place the spacecraft into an earth-to-moon orbit 22.

Near the moon 14, a change in velocity is provided to reduce thespacecraft's moon-relative energy and transfer the spacecraft into amoon-relative orbit 24 which is not necessarily circular. An additionalchange in velocity is then provided to transfer the spacecraft from themoon-relative orbit 24 to the moon 14 by way of the moon landingtrajectory 25. When an earth-return is desired, a change in velocitysufficient to place the spacecraft into a moon-to-earth orbit 26 isprovided either directly from the moon's surface or through multipleimpulses as in the descent. Finally, near the earth 16, a change invelocity is provided to reduce the spacecraft's earth-relative energyand return the spacecraft to low earth orbit 20 or to earth 16 via theearth-return trajectory 27.

FIG. 4 is an illustration of another conventional orbital system,described in U.S. Pat. No. 5,158,249 to Uphoff, incorporated herein byreference, including the references cited therein. The orbital system 28comprises a plurality of earth-relative orbits, where transfertherebetween is accomplished by using the moon's gravitational field.The moon's gravitation field is used by targeting, through relativelysmall mid-orbit changes in velocity, for lunar swingby conditions whichyield the desired orbit.

Although the earth-relative orbits in the orbital system 28 may beselected so that they all have the same Jacobian constant, thusindicating that the transfers therebetween can be achieved with nopropellant-supplied change in velocity in the nominal case, relativelysmall propellant-supplied changes in velocity may be required.Propellant-supplied changes in velocity may be required to correct fortargeting errors at previous lunar swingbys, to choose betweenalternative orbits achievable at a given swingby, and to account forchanges in Jacobian constant due to the eccentricity of the moon'searth-relative orbit 36.

In FIG. 4, a spacecraft is launched from earth 16 or low earth orbitinto an earth-to-moon orbit 22. The earth-to-moon orbit 22 may comprise,for example, a near minimal energy earth-to-moon trajectory, forexample, an orbit having an apogee distance that nearly matches themoon's earth-relative orbit 36 radius. The spacecraft encounters themoon's sphere of gravitational influence 30 and uses the moon'sgravitational field to transfer to a first earth-relative orbit 32.

The first earth-relative orbit 32 comprises, for example, approximatelyone-half revolution of a substantially one lunar month near circularorbit which has a semi-major axis and eccentricity substantially thesame as the moon's earth-relative orbit 36, which is inclinedapproximately 46.3 degrees relative to the plane defined by the moon'searth-relative orbit 36, and which originates and terminates within themoon's sphere of influence 30. Because the first earth-relative orbit 32and a typical near minimum energy earth-to-moon orbit 22 have the sameJacobian constant, the transfer can be accomplished by using the moon'sgravitational field.

FIG. 5 is an illustration of another orbital system where, for example,satellites orbit the earth. A central station SC is situated at thecenter of a spherical triangle-shaped covering zone Z. Twogeosynchronous satellites S-A and S-B have elliptical orbits withidentical parameters. These parameters may be, for example, thefollowing:

apogee situated at about 50,543.4 km,

perigee situated at about 21,028.6 km,

meniscal axis of 42,164 km,

inclination of 63 degrees,

perigee argument 270,

orbit excentricity 0.35.

Each satellite includes an antenna or antennae 11 and 11 a; each antennais orientated towards the central station throughout the period when thesatellite moves above the covering zone. The central station includesone connection station and one control station. FIG. 5 also shows amobile unit M (which is situated inside zone Z, but which is shown abovethe latter for the sake of more clarity). This mobile unit is equippedwith an antenna 14 a whose axis continuously points substantiallytowards the zenith.

In order to station such satellites, a large number of strategies arepossible. One exemplary strategy is described with reference to FIG. 6.This strategy uses the ARIANE IV rocket and requires three pulses. Atthe time of launching, the satellite is accompanied by an ordinarygeostationary satellite. The two satellites are placed on the standardtransfer orbit of the ARIANE IV rocket, this orbit being situated withina quasi-equatorial plane (inclination of 7 degrees) with a perigee at200 km, an apogee at 35,975 km and a perigee argument of 178 degrees.The orbit is marked as OST on FIG. 6.

Close to the perigee, a satellite rocket is ignited for a first pulsesuitable for raising the apogee to 98,000 km, the orbit remaining withinthe same plane, orbit 01. This pulse may be broken down into two orthree pulses. Close to the apogee of the orbit 01, a new pulse is sentto the satellite to change the plane of its orbit. The inclination ofthis plane is close to that of the plane of the definitive orbit, namely63 degrees. This thrust is the largest and may be broken down into twoor three thrusts. The orbit then becomes 02.

Finally, at an appropriate point of this orbit, a third thrust is sentto the satellite so as to provide it with a definitive orbit. If thisstrategy is satisfactory in certain respects, it nevertheless doesconstitute a drawback. In fact, it requires that the orbital plane betilted when passing from the orbit 01 to the orbit 02, this resulting ina considerable consumption of propellant.

FIG. 7 is an illustration of another conventional lunar gravitationalassistance transfer principle. In FIG. 7, the satellite is firstlytransferred onto a standard orbit 01 situated inside a quasi-equatorialplane, which, in practice, is the orbit OST of FIG. 6, known as aGeostationary Transfer Orbit (GTO) orbit. At T1, the satellite istransferred onto a circumlunar orbit 02, still situated in thequasi-equatorial plane.

In practice, an extremely elliptic orbit is selected whose major axis isclose to twice the Earth/Moon distance, namely about 768,800 km. Thesatellite penetrates into the sphere of influence SI of the moon andleaves this sphere on a trajectory 03 whose plane is highly inclinedwith respect to the equatorial plane. At T2, the satellite is injectedonto the definitive orbit 04 inside the same plane as the orbit 03. Theabove described orbital system is described in detail in U.S. Pat. No.5,507,454 to Dulck, incorporated herein by reference, including thereferences cited therein.

Dulck attempts to minimize the thrusters needed, where the standardtechnique of lunar gravity assist is used. The satellite is firstbrought to a neighborhood of the moon by a Hohmann transfer. It thenflies by the moon in just the right directions and velocities, where itis broken up into two or more maneuvers. This method works, but the sizeof this maneuver restricts the applications of the method to ellipseswhose eccentricities are sufficiently large. This is because to have asavings with this large maneuver, the final maneuver needs to besufficiently small.

I have determined that all of the above orbital systems and/or methodssuffer from the requirement of substantial fuel expenditure formaneuvers, and are therefore, not sufficiently efficient. I have alsodetermined that the above methods focus on orbital systems thatconcentrate on the relationship between the earth and the moon, and donot consider possible effects and/or uses beyond this two-body problem.

Accordingly, it is desirable to provide an orbital system and/or methodthat furnishes efficient use of fuel or propellant. It is also desirableto provide an orbital system and/or method that it not substantiallydependent on significant thrusting or propelling forces.

It is also desirable to provide an orbital system and/or method thatconsiders the effects of lunar capture and/or earth capture as more thanmerely a two body problem. It is also desirable to provide an orbitalsystem and/or method that may be implemented on a computer system thatis either onboard the spacecraft or satellite, or located in a centralcontrolling area.

It is also desirable to provide an orbital system and/or method thatallows a spacecraft to make repeated close approaches to both the earthand moon. It is also desirable to provide an orbital system and/ormethod that is sustainable with relatively low propellant requirements,thereby providing an efficient method for cislunar travel.

It is also desirable to provide an orbital system and/or method thatdoes not require large propellant supplied changes in velocity. It isalso desirable to provide an orbital system and/or method that renderspractical massive spacecraft components. It is also desirable to providean orbital system and/or method that may be used for manned and unmannedmissions.

SUMMARY OF THE INVENTION

It is a feature and advantage of the present invention to provide anorbital system and/or method that furnishes efficient use of fuel orpropellant.

It is another feature and advantage of the present invention to providean orbital system and/or method that it not substantially dependent onsignificant thrusting or propelling forces.

It is another feature and advantage of the present invention to providean orbital system and/or method that considers the effects of lunarcapture and/or earth capture as more than merely a two body problem.

It is another feature and advantage of the present invention to providean orbital system and/or method that may be i implemented on a computersystem that is either onboard the spacecraft or satellite, or located ina central controlling area.

It is another feature and advantage of the present invention to providean orbital system and/or method that allows a spacecraft to makerepeated close approaches to both the earth and moon.

It is another feature and advantage of the present invention to providean orbital system and/or method that is sustainable with relatively lowpropellant requirements, thereby providing an efficient method forcislunar travel.

It is another feature and advantage of the present invention to providean orbital system and/or method that does not require large propellantsupplied changes in velocity.

It is another feature and advantage of the present invention to providean orbital system and/or method that renders practical massivespacecraft components.

It is another feature and advantage of the present invention to providean orbital system and/or method that may be used for manned and unmannedmissions.

The present invention comprises a system and/or method for cislunartravel which substantially reduces the propellant requirements for lunarmissions. The present invention also provides orbital systems useful forearth-to-moon and moon-to-earth travel, which do not directly utilizethe moon's gravitational field to achieve orbital transfers and can besustained with relatively low propellant requirements. The presentinvention further provides frequent earth return possibilities forequipment and personnel on the moon, or in a moon-relative orbit.

The present invention is based, in part, on my discovery that theconventional methods and/or orbital systems that concentrate or revolvearound the relationship between the earth and the moon, and do notconsider possible effects and/or uses beyond this two-body problem. Morespecifically, I have determined a new method and system that considerslunar travel and/or capture at least a three-body problem. This at leastthree-body problem includes the inter-relationship between the earth,moon and sun, including the inter-relationship of gravitational forcesrelated thereto.

In accordance with one embodiment of the invention, a method generatesan operational ballistic capture transfer for an object emanatingsubstantially at earth or earth orbit to arrive at the moon or moonorbit using a computer implemented process. The method includes thesteps of entering parameters including velocity magnitude V_(E), flightpath angle γ_(E), and implementing a forward targeting process byvarying the velocity magnitude V_(E), and the flight path angle γ_(E)for convergence of target variables at the moon. The target variablesinclude radial distance, r_(M), and inclination i_(M). The method alsoincludes the step of iterating the forward targeting process untilsufficient convergence to obtain the operational ballistic capturetransfer from the earth or the earth orbit to the moon or the moonorbit.

There has thus been outlined, rather broadly, the more importantfeatures of the invention in order that the detailed description thereofthat follows may be better understood, and in order that the presentcontribution to the art may be better appreciated. There are, of course,additional features of the invention that will be described hereinafterand which will form the subject matter of the claims appended hereto.

In this respect, before explaining at least one embodiment of theinvention in detail, it is to be understood that the invention is notlimited in its application to the details of construction and to thearrangements of the components set forth in the following description orillustrated in the drawings. The invention is capable of otherembodiments and of being practiced and carried out in various ways.Also, it is to be understood that the phraseology and terminologyemployed herein are for the purpose of description and should not beregarded as limiting.

As such, those skilled in the art will appreciate that the conception,upon which this disclosure is based, may readily be utilized as a basisfor the designing of other structures, methods and systems for carryingout the several purposes of the present invention. It is important,therefore, that the claims be regarded as including such equivalentconstructions insofar as they do not depart from the spirit and scope ofthe present invention.

Further, the purpose of the foregoing abstract is to enable the U.S.Patent and Trademark Office and the public generally, and especially thescientists, engineers and practitioners in the art who are not familiarwith patent or legal terms or phraseology, to determine quickly from acursory inspection the nature and essence of the technical disclosure ofthe application. The abstract is neither intended to define theinvention of the application, which is measured by the claims, nor is itintended to be limiting as to the scope of the invention in any way.

These together with other objects of the invention, along with thevarious features of novelty which characterize the invention, arepointed out with particularity in the claims annexed to and forming apart of this disclosure. For a better understanding of the invention,its operating advantages and the specific objects attained by its uses,reference should be had to the accompanying drawings and descriptivematter in which there is illustrated preferred embodiments of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an integrable system with two degrees of freedom on atorus, and a closed orbit of a trajectory;

FIG. 2 illustrates a set of KAM invariant tori on the surface of whichlie as elliptic integrable solutions;

FIG. 3 is an illustration of an orbital system in accordance with aconventional lunar mission in a non-rotating coordinate system;

FIG. 4 is an illustration of another conventional orbital system;

FIG. 5 is an illustration of another orbital system where, for example,satellites orbit the earth;

FIG. 6 is an illustration of another orbital system where, for example,satellites are placed in orbit about earth using the ARIANE IV rocketthat requires three pulses;

FIG. 7 is an illustration of another conventional lunar gravitationalassistance transfer principle;

FIG. 8 is an illustration of a forward integration method so the endstate of the forward integration matches the beginning state determinedby the backwards integration;

FIG. 9 is an illustration of an operational BCT determined by theforwards integration in accordance with the present invention;

FIG. 10 is another illustration of an operational BCT determined by theforwards integration in accordance with the present invention;

FIG. 11 is a conceptual illustration of a flowchart of the interactionbetween the Numerical Integrator and the Initial Condition Generator;

FIG. 11A is a detailed illustration of a flowchart of the interactionbetween the Numerical Integrator and the Initial Condition Generator;

FIG. 11B is another detailed illustration of a flowchart of theinteraction between the Numerical Integrator and the Initial ConditionGenerator;

FIG. 12 is an illustration of a summary of various lunar missions;

FIG. 13 is an illustration of main central processing unit forimplementing the computer processing in accordance with one embodimentof the present invention;

FIG. 14 is a block diagram of the internal hardware of the computerillustrated in FIG. 13; and

FIG. 15 is an illustration of an exemplary memory medium which can beused with disk drives illustrated in FIGS. 13-14.

NOTATIONS AND NOMENCLATURE

The detailed descriptions which follow may be presented in terms ofprogram procedures executed on a computer or network of computers. Theseprocedural descriptions and representations are the means used by thoseskilled in the art to most effectively convey the substance of theirwork to others skilled in the art.

A procedure is here, and generally, conceived to be a self-consistentsequence of steps leading to a desired result. These steps are thoserequiring physical manipulations of physical quantities. Usually, thoughnot necessarily, these quantities take the form of electrical ormagnetic signals capable of being stored, transferred, combined,compared and otherwise manipulated. It proves convenient at times,principally for reasons of common usage, to refer to these signals asbits, values, elements, symbols, characters, terms, numbers, or thelike. It should be noted, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities.

Further, the manipulations performed are often referred to in terms,such as adding or comparing, which are commonly associated with mentaloperations performed by a human operator. No such capability of a humanoperator is necessary, or desirable in most cases, in any of theoperations described herein which form part of the present invention;the operations are machine operations. Useful machines for performingthe operation of the present invention include general purpose digitalcomputers or similar devices.

The present invention also relates to apparatus for performing theseoperations. This apparatus may be specially constructed for the requiredpurpose or it may comprise a general purpose computer as selectivelyactivated or reconfigured by a computer program stored in the computer.The procedures presented herein are not inherently related to aparticular computer or other apparatus. Various general purpose machinesmay be used with programs written in accordance with the teachingsherein, or it may prove more convenient to construct more specializedapparatus to perform the required method steps. The required structurefor a variety of these machines will appear from the description given.

DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

When a rocket travels from the earth to the moon on a classical directroute taking only three days called a Hohmann transfer, it must fire itsengines in order to slow down to achieve lunar orbit. Otherwise, therocket will overfly the moon at about 1 km/s. A typical lunar missioncomprises the following steps. Initially, a spacecraft is launched fromearth or low earth orbit with sufficient impulse per unit mass, orchange in velocity, to place the spacecraft into an earth-to-moon orbit.Generally, this orbit is a substantially elliptic earth-relative orbithaving an apogee selected to nearly match the radius of the moon'searth-relative orbit.

As the spacecraft approaches the moon, a change in velocity is providedto transfer the spacecraft from the earth-to-moon orbit to amoon-relative orbit. An additional change in velocity may then beprovided to transfer the spacecraft from the moon-relative orbit to themoon's surface if a moon landing is planned. When a return trip to theearth is desired, another change in velocity is provided which issufficient to insert the spacecraft into a moon-to-earth orbit, forexample, an orbit similar to the earth-to-moon orbit. Finally, as thespacecraft approaches the earth, a change in velocity is required totransfer the spacecraft from the moon-to-earth orbit to a low earthorbit or an earth return trajectory.

The propellant required at each step above depends on the mass of thespacecraft and the change of velocity required to effect the orbitaltransfer. The change in velocity at each step is generally provided byburning propellant. A mass of propellant is thereby expelled from thespacecraft at a large spacecraft-relative velocity, and the remainingspacecraft mass changes velocity reactively. As a practical matter,because the orbital transfers in prior art lunar missions are achievedby burning propellant, the number and magnitude of orbital transferswhich can be performed in a lunar mission are highly sensitive to themass of the spacecraft.

It had been always assumed that it was not realistically possible to becaptured at the moon without requiring slowing down using the engines.The present invention comprises a system and/or method for cislunartravel which substantially reduces the propellant requirements for lunarmissions. The present invention also provides orbital systems useful forearth-to-moon and moon-to-earth travel, which do not directly utilizethe moon's gravitational field to achieve orbital transfers and can besustained with relatively low propellant requirements. The presentinvention further provides frequent earth return possibilities forequipment and personnel on the moon, or in a moon-relative orbit.

When a spacecraft arrives at the Moon from a Hohmann transfer, it has ahyperbolic excess velocity of approximately 1 km/s. Thus, to be capturedinto an elliptic lunar orbit, the spacecraft, S/C, must be slowed by theuse of the propulsion system. The amount of propellant to do this can besignificant and, moreover, there is a relatively short period of timefor the braking maneuver to accomplish the lunar capture. The ability toachieve capture, that is for a S/C to have an elliptic orbital statewith respect to the Moon at lunar periapsis, without the use of brakingrockets is called ballistic capture.

Belbruno first found a way to do this in 1986 for an electric propulsionspacecraft mission study called LGAS (Lunar Get Away Special), Belbruno,E., Lunar Capture Orbits, a Method of Constructing Earth-MoonTrajectories and the Lunar GAS Mission, AIAA Paper no. 97-1054,Proceedings of AIAA/DGLR/JSASS Inter. Elec. Propl. Conf., May 1987,incorporated herein by reference including the references cited therein.This was accomplished realizing that in order for ballistic capture tooccur, the S/C must arrive at the Moon in a weakly captured state. Thatis, the S/C must have a velocity at the desired capture radius where itis balancing between capture and escape. A region can be estimated aboutthe Moon where this occurs, and it is called the Weak Stability Boundary(WSB) or the Fuzzy Boundary, Belbruno, E., Lunar Capture Orbits, aMethod of Constructing Earth-Moon Trajectories and the Lunar GASMission, AIAA Paper no. 97-1054, Proceedings of AIAA/DGLR/JSASS Inter.Elec. Propl. Conf., May 1987; Belbruno, E., Example of the NonlinearDynamics of Ballistic Capture and Escape in the Earth-Moon System, AIAAPaper No. 90-2896, Proceedings of the Annual AIAA AstrodynamicsConference, August 1990; Belbruno, E.; Miller, J., Sun-PerturbedEarth-to-Moon Transfers with Ballistic Capture, Journal of Guidance,Control, and dynamics, V.16, No. 4, July-August 1993. pp 770-775;Belbruno, E., Ballistic Lunar Capture Transfers using the Fuzzy Boundaryand Solar Perturbations: A Survey, Journal of the British InterplanetarySociety, v. 47, January 1994, pp 73-80; Belbruno, E., The DynamicalMechanism of Ballistic Lunar Capture Transfers in The Four-Body ProblemFrom The Perspective of Invariant Manifolds and Hill's Regions, CentreDe Recreca Matematica (CRM) Preprint n. 270, December 1994, all of whichare hereby incorporated by reference including the references citedtherein.

Once the WSB is estimated, the problem of ballistic capture reduces tothe problem of reaching this region (i.e. arrive at the Moon at thedesired altitude with the correct velocity). Because the WSB liesbetween capture and escape, the S/C does not have a well defined centralbody—the Earth or the Moon. Thus its motion is quite sensitive. Becauseof this, it seemed at the time that a forward Newton targeting search tothis region from near the Earth would not be successful. This indeedseemed to be true.

It was solved by the backwards method, suggested by D. Byrnes in 1986.This has been used to find precision BCT's for actual missions andmission studies ever since starting with LGAS, then Hiten in 1990, LunarObserver in 1990, the planned Lunar-A, and, until late 1996, Blue Moon.See, e.g., Yamakawa, H.; Kawaguchi, J.; Ishii, N.; Matsuo, H., OnEarth-Moon Transfer Trajectory with Gravitational Capture, ProceedingsAAS/AIAA Astrodynamics Sp. Conf., Paper No. AAS 93-633, August 1993;Kawaguchi, J.; Yamakowa, H.; Uesugi, T.; Matsuo, H., On Making Use ofLunar and Solar Gravity Assists in Lunar-A, Planet-B Missions, Acta.Astr., V. 35, pp 633-642, 1995; Cook, R. A.; Sergeyevsky, A. B.;Belbruno, E.; Sweetser, T. H.; Return to the Moon; The Lunar ObserverMission, Proceedings AIAA/AAS Astrodynamics Conf., Paper No. 90-288,August 1990; Sweetser, T., Estimate of the Global Minimum DV Needed forEarth-Moon Transfers, Proceedings AAS/AIAA Spaceflights MechanicsMeeting, Paper No. 91-101, February 1991; Humble, R. W., Blue Moon; ASmall Satellite Mission to the Moon, Proceedings Int.Symp. on SmallSatellite Systems and Services, Annecy, France, June 1996, all of whichhereby incorporated by reference herein including all the referencescited therein, and references previously incorporated herein.

The backwards method starts at the desired capture position y withrespect to the WSB at the Moon where the osculating eccentricitye_(M)<1. Using this as the initial position, one integrates in backwardstime. Because of the sensitivity of the region, a negligible increase invelocity at y will cause the S/C to escape the Moon in backwards time.It will have a periapsis at a point x with respect to the Earth wherethe integration is stopped. In general, this point will be differentfrom the starting point x_(o) for the S/C.

The BCT is then found by performing a forward integration from x_(o) tox. The path from x to the capture point y is already determined. Thegain made in the ΔV savings due to ballistic capture is offset by themismatch in velocity at x requiring a maneuver ΔV_(M). This isabstractly shown in FIG. 8. Variation of different parameters are usedto try and reduce the ΔV_(M).

In the case of LGAS, x_(o) is at 200 km altitude from the Earth, and xis at 100,000 km. The point y is 30,000 km over the north lunar pole.The S/C takes about one year to gradually spiral out to x using its lowthrust ion engines, where ΔV_(M) is zero. The portion of the transferfrom x to y in the WSB where e_(M)=0 takes 14 days.

The method was used again by Belbruno, assisted by J. Miller in 1990 forthe Hiten mission of Japan. See previous references incorporated byreference herein. Hiten did not have sufficient propellant to becaptured at the Moon by the Hohmann transfer, so the BCT was the onlyoption. It was in elliptic Earth orbit where the periapsis radicaldistance was 8,900 km at x_(o). The capture position y in the WSB was100 km over the north lunar pole, where the osculating value of theeccentricity e_(M)=0.94.

Under the influence of solar perturbations, backwards integration from ypulled the S/C out to an Earth periapsis at x, 1.2 million km from theEarth. A tiny ΔV of 14 m/s at x_(o) was sufficient to allow Hiten tomove to x where ΔV_(M)=30 m/s. The time of flight was 150 days. This BCTwas used in 1991, and Hiten arrived at the Moon on October 2 of thatyear.

This type of BCT used by Hiten can be used for general lunar missionswhere injection conditions at the Earth and capture conditions at theMoon are arbitrary. To make it more applicable to general missions, thebackwards approach would have to be generalized and made to be moreflexible. Joint work form 1992-1993 discovered a way to adapt thebackwards approach for general missions, including finding launchperiods. Tandon, S., Lunar Orbit Transfers using Weak Stability BoundaryTheory, McDonnell Douglas Internal Report (Huntington Beach), March1993. However, it is unwieldy and seemingly difficult to automate. Thisis because one has to generally satisfy six orbital elements at theEarth.

We focused on BCT's with no maneuvers at x. By carefully adjusting thelunar capture WSB conditions at y, it is not difficult to adjust thebackwards integration so that the trajectory comes back to the Earth atany desired altitude r_(E), at x_(o). In fact, variation of e_(M) in theWSB in the third and higher decimal places is sufficient for this. Thetime of flight is only 80 days. However, when doing this, one has nocontrol over the inclination, i_(E). If one starts at x_(o) and thentries to walk the inclination over to the desired value, it was seenimmediately that it did not seem to be possible. Even a change in i_(E)in the thousandths place causes the forward targeting algorithm todiverge when targeting back to the WSB conditions.

This can be solved by a more involved backwards integration whereseveral lunar variables, Ω_(M) (ascending node), ω_(M) (argument ofperiapsis), e_(M), have to be varied to achieve both the correct ofr_(E), i_(E). However, the variables Ω_(E), ω_(E) remain to besatisfied. The procedure to do this is complicated and involves thecomparison of many contour plots of the Earth elements, and backwardsintegrations. Eventually they can be satisfied. However, the approach istime intensive.

I have found, however, a set of variables with respect to the earthwhich give rise to a very flexible and well behaved forward targeting toballistic capture lunar conditions using two variables at the Earth tovary, where the variables do not change in the process. These variablesare

1. velocity magnitude,

2. flight path angle.

I have also discovered a way to efficiently find BCT's in a relativelysimple forward targeting method from x_(o) to y which is fairly robust.This forward method turns out to be 2×2. That is, two variables at theEarth are varied in a Newton's targeting algorithm to achieve WSBconditions at the Moon using two lunar elements. In carrying it out,most of the variables of interest at the Earth decouple in the process.This gives control on r_(E), i_(E), Ω_(E). Several examples are givenbelow.

In order to have a robust search from the Earth at a given point x_(o),to WSB conditions at the Moon at y, the algorithm should be able toconverge down to a BCT with large initial errors in achieving thedesired lunar conditions. The independent variables being varied atx_(o) to achieve these lunar conditions should be decoupled from as manyangular Earth elements as possible which include i_(E), Ω_(E), ω_(E). Itis assumed that search is done with a time from periapsis, T_(E),approximately equal to zero. All three of these angular variables can bequite constrained depending on the launch vehicle. For example, for anArianne IV, i_(E)=7E, Ω_(E)≈8° (West), ω_(E)=178E.

The target variables at the Moon of main interest to satisfy are theradial distance, r_(M), and the inclination, i_(M). For the Blue Moonmission, we assume r_(M)=2238 km, representing an altitude of 500 km,and i_(M)=90E. It turns out that if the S/C falls towards the Moon fromapproximately 1 to 1.5 million km form the Earth near an Earth apoapsisin approximately the ecliptic, then it falls into the lunar WSB providedthe Earth-Moon-Sun geometry is correct.

The coordinate system at the Earth required for the targeting algorithmat X_(E) is spherical coordinates. They are given by r_(E), longitude,α_(E), latitude, δ_(E), velocity magnitude, V_(E), flight path angle,γ_(E), flight path azimuth, σ_(E). The flight path azimuth is the anglefrom the positive z-axis of the local Cartesian coordinate system to thevelocity vector V_(E)=(x,y,z). More exactly,

σ_(E)=cos⁻(z/V _(E))

We fix r_(E)=6563.94 km corresponding to an altitude of 186 km for theBlue Moon. The targeting algorithm is given by varying V_(E), γ_(E) totry to achieve r_(M), i_(M). A standard second order Newton algorithm isused. Symbolically,

V _(E), γ_(E) →r _(M) , i _(M)  (1)

It is checked that i_(E), Ω_(E) are independent of V_(E), γ_(E). Thus,the 2×2 search defined by (1) does not alter i_(E), Ω_(E). As a result,once (1) converges to a BCT, for a given i_(E), Ω_(E), these can bechanged and (1) can be rerun. This is done by taking the convergedvalues of V_(E), γ_(E) together with the other four fixed sphericalvariables, and transforming them to classical elements. In the classicalelements, i_(E), Ω_(E) are changed as desired.

The classical state is then transformed back to spherical coordinates.The new spherical state will still have the same converged values ofV_(E), γ_(E) (since V_(E), γ_(E) are independent of i_(E), Ω_(E)),however, α_(E), δ_(E), σ_(E) will be changed. If this is not too much,the (1) should converge. In this way i_(E), Ω_(E) can be systematicallywalked over to their desired values by rerunning (1) a finite number oftimes.

The remaining variable that there has been no control over is ω. Thereare several approaches that could be used to adjust this variable. Theserange from variation of the Earth injection date (I/D), to the use ofcontours, or the inclusion of a maneuver. It is, in general, a good ideato construct contours of the time of flight (T_(f)), i_(E), Ω_(E), ω_(E)by variation of Ω_(M), ω_(M). The data for these contours is generatedby systematically varying Ω_(M), ω_(M) and for each different variation,adjusting e_(M) so that the trajectory in backward time returns to Earthat the same radial distance. That is, by 1×1 Newton targeting e_(M) 6r_(E).

For each value of (Ω_(M), ω_(M)), the value of (T_(f), i_(E), Ω_(E),ω_(E)) is recorded. These arrays can be used in any number of contourprograms. The contours of these variables can be useful in determiningregions of the parameter space, including I/D, where the desired valuesof i_(E), Ω_(E), ω_(E) can be found.

It is noted that to start the procedure, a good guess for V_(E), γ_(E)and the other spherical variables needs to be found so (1) converges.There are many ways to do this. One thing to do is to go to classicalelements, and choose a_(E), e_(E) so that the S/C is on an ellipse of anapoapsis between 1 and 1.5 million km, and that the periapsis distanceis at the desired altitude. For example, realistic values are a=657,666km, e=0.9900. The other variables can be manually tested to see ifconvergence of (1) results.

The robustness of (1) is illustrated in Table 1 which represents achange of i_(E) by two degrees from a previously converged case withi_(E)=21.56E (EME of Date) to 19.56E. Throughout the search,Ω_(E)=36.51E. Although there is a huge miss distance of 252,243 km onthe first iteration, convergence still results. The resulting time offlight on the converged iteration was 93 days, 5 hours, 13 minutes.

TABLE 1 Targeting Iterations Iteration e_(M) V_(E) γ_(E) r_(M) i_(M) 110.992708088 1.310755264 252243.45 157.23 1.79 2 10.9929963821.310755164 59489.90 54.70 .21 3 10.992972418 1.310755175 36675.56 56.85.32 4 10.992950388 1.310755214 11753.77 54.34 .62 5 10.9929285401.310604119 6286.67 67.74 .80 10 10.992752082 0.906403936 2237.74 89.93.93 11 10.992751828 0.905723383 2241.06 90.03 .93 12 10.9927518190.905724637 2238.00 90.00 .93

This section is concluded with the documentation of a BCT for Blue Moonwhich is designed for an Arianne IV launch vehicle:

1. Earth Injection

T: Jul. 16, 1997 06:16:55 (ET)

r_(E)=6563.94 km

V_(E)=10.99 km/s

i_(E)=7E

2. Apoapsis

T: Aug. 22, 1997 11:48:08

r_(E)=1,370,923 km

V_(E)=0.215 km/s

3. Lunar Capture

T: Oct. 19, 1997 06:52:47

r_(M)=2238.00 km

V(Moon)=2.08 km/s

a_(M)=84,217.12 km

e_(M)=0.97

i_(M)=90E

This BCT is plotted in FIG. 9.

FIG. 10 is another illustration of an operational BCT determined by theforwards integration in accordance with the present-invention. In FIG.10, the ballistic lunar capture trajectory is illustrated. Leg 1 of thetrajectory begins at the earth, substantially near the earth or at anorbit around the earth and extends until the earth-sun weak stabilityboundary. Maneuver 1 is associated with leg 1, and may be, for example,11 meters per second (m/s) at the earth-sun WSB. Alternatively, thethrust may be designed such that at the earth-sun WSB, the object in thetrajectory is going faster than 11 m/s or even arrives at the earth-sunWSB at zero m/s.

The object passes the moon area approximately three day later along leg1. In addition, the object arrives at the end of leg 1 approximately oneand a half months later. At the earth-sun WSB, a second maneuver isperformed for leg 2 of the journey which takes the object from theearth-sun WSE to lunar capture around the moon. This time period takesapproximately another three months for leg 2.

Whereas the backwards integration approach took one month of daily fulltime work to find an operational BCT, this new procedure with forwardtargeting, takes a few minutes on a computer. It can easily be automatedto walk i, Ω, ω over to their desired values. However, this is easilydone manually. It is noted that the targeting procedure is only a 2×2.That is, two control variables and two target variables. Given thenature of the BCT, this is an elegant procedure.

The software required to do this is

1. Numerical integrator with targeting capability,

2. Initial condition generator.

See FIG. 11 for a flowchart of the interaction between the NumericalIntegrator 102 and the Initial Condition Generator IGUESS 100 inaccordance with the present invention.

The integrator is extremely accurate and is a standard 10th order, orother standard integrator. The targeter is a standard second orderNewton's method. This integrator models the solar system as accuratelyas is scientifically available, and uses a planetary ephemeris. Thisaccuracy is necessary since this procedure produces operationaltransfers that are suitable for real missions and flight.

The trajectories generated by the integrator are found to be innegligible error with the actual paths of the spacecraft. Theintegrator-targeter is in stand-alone source code and is written inFORTRAN. This integrator-targeter software is included in U.S.provisional application serial No. 60/036,864, incorporated herein byreference. The initial condition generator produces a good initial guessin the desired targeting variables in spherical coordinates, and allowsincremental change in i, Ω, ω. This is needed so that the targeter canconverge.

The integrator-targeter requires a precise planetary ephemeris of themotions of the planets. It is the standard data file for the planetsproduced at JPL and is called DE403, incorporated herein by reference.It is used throughout the world for astronomers and in aerospace.

FIG. 11A is a detailed illustration of a flowchart of the interactionbetween the Numerical Integrator and the Initial Condition Generator. Asillustrated in FIG. 11A, the procedure of the present invention uses twodifferent types of variables in the targeted search, using a secondorder Newton's method (NM) 104 for the targeter, and a 10th orderintegrator (I) 106 to numerically propagate an orbit (or trajectory)from the earth to the moon. A 2×2 search is used for the targeter(although other dimensional searches may also be used), i.e., twovariables (out of 6) are varied at the earth, and target to two at themoon (out of six).

At the moon, two parameters are enough. They are i_(M), r_(M). For thetargeter, a special set of 6 variables are preferably used, calledspherical coordinates, and two of these are selected to vary to reachi_(M), r_(M) (of course, the present invention also includes the use ofdifferent variables that are derivable from the present invention). Thesix variables are r_(E), α_(E), s_(E), v_(E), γ_(E), σ_(E). The two thatare actually varied are v_(E), γ_(E). With a good guess for v_(E), σ_(E)the targeter converges. IGESS 100 determines a good initial guess forv_(E), γ_(E).

The targeter incorporates the integrator as it operates. It needs to useintegrator I multiple times as it operates. Its goal is to iterativelydetermine the accurate value of v_(E), γ_(E)=v_(E)*, so that a BCTreaches the moon to the desired values of r_(M), i_(M). Only one guessfrom IGESS is required at the very start of the targeting process.

FIG. 11B is another detailed illustration of a flowchart of theinteraction between the Numerical Integrator and the Initial ConditionGenerator. The BCT just produced goes from the Earth at a given orbitalstate to the moon where r_(M), i_(M) are achieved to their desiredvalues. In the process described in FIG. 11B, only v_(E), γ_(E) arevaried, and the other four variables r_(E),α_(E), e_(E),σ_(E,) arefixed. Our six variables determined are therefore r_(E), α_(E), S_(E),v_(E)*, γ_(E)*, γ_(E).

To make an operational BCT, 6 orbital parameters making what?s called anorbital state, are required at the earth. They are given ahead of timeby a mission, and must all be satisfied. The variables usually need tosatisfy another set of variables, related to the above ones, butdifferent. They are called classical elements, and are α_(E), e_(E),i_(E), Ω_(E), ω_(E)T_(E). The above converged state, S=r_(E), α_(E),s_(E), v_(E)*, γ_(E)*, σ_(E) will yield a specific set of classicalvariables C=α_(E), e_(E), i_(E), Ω_(E), W_(E), T_(E).

In general, the values of the classical variables will not be what themission may require. A mission will want a specific i_(E)=i_(E)*, Ω_(E),W_(E)*. These are usually trick to nail down. The others, α_(E), e_(E),T_(E), are easy to determine, and not really an issue. If, as v_(E),γ_(E) varied in NM, i_(E), Ω_(E) varied, that would be a complication.However, i_(E), Ω_(E) are independent of v_(E), γ_(E), so they remainfixed as NM converges. Thus, after NM converges, i_(E), Ω_(E) can beupdated to a slightly different value, and NM should converge again. Byiteratively doing this, i_(E), Ω_(E) can be gradually walked over totheir desired values, after applying FIG. 11A many times. The best wayto vary i_(E), Ω_(E) can be guided by knowing the contour space of C,which can be determined by standard contour programs (e.g., CONTcommercial program). The final variable left is W_(E) which does vary asNM operates. However, it varies little and can also be walked over toits desired value.

In summary, the process described in FIG. 11B is reiterated or reapplieduntil i_(E), Ω_(E) are walked over to desired values. A standard contourprogram is used to assist in this. Finally, walk over WE to its desiredvalue by reapplying the process described in FIG. 11B a sufficientnumber of times.

FIG. 13 is an illustration of main central processing unit 218 forimplementing the computer processing in accordance with one embodimentof the present invention. In FIG. 13, computer system 218 includescentral processing unit 234 having disk drives 236 and 238. Disk driveindications 236 and 238 are merely symbolic of the number of disk driveswhich might be accommodated in this computer system. Typically, thesewould include a floppy disk drive such as 236, a hard disk drive (notshown either internally or externally) and a CD ROM indicated by slot238. The number and type of drives varies, typically with differentcomputer configurations. The computer includes display 240 upon whichinformation is displayed. A keyboard 242 and a mouse 244 are typicallyalso available as input devices via a standard interface.

FIG. 14 is a block diagram of the internal hardware of the computer 218illustrated in FIG. 13. As illustrated in FIG. 14, data bus 248 servesas the main information highway interconnecting the other components ofthe computer system. Central processing units (CPU) 250 is the centralprocessing unit of the system performing calculations and logicoperations required to execute a program. Read-only memory 252 andrandom access memory 254 constitute the main memory of the computer, andmay be used to store the simulation data.

Disk controller 256 interfaces one or more disk drives to the system bus248. These disk drives may be floppy disk drives such as 262, internalor external hard drives such as 260, or CD ROM or DVD (digital videodisks) drives such as 258. A display interface 264 interfaces withdisplay 240 and permits information from the bus 248 to be displayed onthe display 240. Communications with the external devices can occur oncommunications port 266.

FIG. 15 is an illustration of an exemplary memory medium which can beused with disk drives such as 262 in FIG. 14 or 236 in FIG. 13.Typically, memory media such as a floppy disk, or a CD ROM, or a digitalvideo disk will contain, inter alia, the program information forcontrolling the computer to enable the computer to perform the testingand development functions in accordance with the computer systemdescribed herein.

Although the processing system is illustrated having a single processor,a single hard disk drive and a single local memory, the processingsystem may suitably be equipped with any multitude or combination ofprocessors or storage devices. The processing system may, in point offact, be replaced by, or combined with, any suitable processing systemoperative in accordance with the principles of the present invention,including sophisticated calculators, and hand-held, laptop/notebook,mini, mainframe and super computers, as well as processing systemnetwork combinations of the same.

Conventional processing system architecture is more fully discussed inComputer Organization and Architecture, by William Stallings, MacMillamPublishing Co. (3rd ed. 1993); conventional processing system networkdesign is more fully discussed in Data Network Design, by Darren L.Spohn, McGraw-Hill, Inc. (1993), and conventional data communications ismore fully discussed in Data Communications Principles, by R. D. Gitlin,J. F. Hayes and S. B. Weinstain, Plenum Press (1992) and in The IrwinHandbook of Telecommunications, by james Harry Green, Irwin ProfessionalPublishing (2nd ed. 1992). Each of the foregoing publications isincorporated herein by reference.

In alternate preferred embodiments, the above-identified processor, andin particular microprocessing circuit, may be replaced by or combinedwith any other suitable processing circuits, including programmablelogic devices, such as PALs (programmable array logic) and PLAs(programmable logic arrays). DSPs (digital signal processors), FPGAs(field programmable gate arrays), ASICs (application specific integratedcircuits), VLSIs (very large scale integrated circuits) or the like.

It is remarked that the starting position from the earth for a BCTcomputed with this procedure can be at any altitude, suitable for anylaunch vehicle, the international space station Alpha, underdevelopment, the revolutionary single stage to orbit vehicle calledVenture Star using a new type of rocket engine under development byLockheed. Utilization of the FB region yields other low energy transfersto asteroids, Mars, and from these locations, using so called resonancehopping.

In summary, this forward targeting procedure to produce operationalBCT's is substantially easier to use and faster than the backwardsapproach. It is a 2×2 procedure and makes the computation of BCT's astraight forward process, and it is robust. The BCT's can be computedfor any starting positions with respect to the earth or arrivalconditions at the moon.

Recent planned missions for the remainder of this decade show that theBCT is becoming the route of choice. Japan plans to use it again in 1998on the so called Lunar-A mission, and the US Air Force Academy plans touse it in 1998-1999 for the so called Blue Moon mission. In fact,components of the Blue Moon mission will be tested in space on a launchof an Atlas rocket on Oct. 21, 1997 from Cape Canaveral. Of the fivelunar missions from 1991-1999, three are using the BCT.

The future for lunar development looks very promising. In the next 10years, there is projected to be billions of dollars spent on lunarmissions. Use of the BCT can cut this cost in half, or equivalently,potentially be the transfer of choice and be responsible for billions ofdollars in lunar missions.

There have been three very important developments which imply that from1999 on, there should be regular and frequent lunar missions, a smalllunar base in about 10 years and then large scale commercial projects.

1. In July 1996, Lockheed was awarded a 1 billion dollar contract todevelop a ⅓ scale version of a single stage to orbit rocket using theaerospike engine. This is the so called X-33 rocket. It willrevolutionize space travel and make flying into space as routine asflying a jet. The smaller version is to be ready in 1998, and the fullscale version in 2002. It is called the Venture Star, and NASA has saidit plans to replace its shuttle fleet with them. Smaller versions willno doubt be commercially available and open up space for the public.

2. In November 1996, water in large easily accessible quantities wasdiscovered on the moon in the south polar regions. This means thatdevelopment of the moon is very likely. This is because water gives aself-sustaining capability.

3. The international space station Alpha starts to go up in Fall of1997, and is to be completed in 2001. This will give a large scalepermanent presence in space, and the station can be used as a launchingplatform.

There are already two lunar missions being planned for 2000, 2001 toinvestigate the lunar water further, and a lot of talk about a smalllunar base. After the Venture Star gets rolling, commercial lunardevelopment is sure to follow with hotels, etc. In fact, Mitsubishi, andother large Japanese corporations have discussed large hotel complexes.See FIG. 12 for a summary of the various lunar missions.

The many features and advantages of the invention are apparent from thedetailed specification, and thus, it is intended by the appended claimsto cover all such features and advantages of the invention which fallwithin the true spirit and scope of the invention. Further, sincenumerous modifications and variations will readily occur to thoseskilled in the art, it is not desired to limit the invention to theexact construction and operation illustrated and described, andaccordingly, all suitable modifications and equivalents may be resortedto, falling within the scope of the invention.

What is claimed is:
 1. A method of generating a capture transfer for anobject emanating substantially at earth or earth orbit to arrive at themoon or moon orbit using a computer implemented process, comprising thesteps of: (a) entering parameters for said method of generating thecapture transfer; (b) implementing a forward targeting process byvarying the parameters for convergence of target variables at the moon;and (c) iterating step (b) until sufficient convergence to obtain thecapture transfer from the earth or the earth orbit to the moon or themoon orbit.
 2. A method of traveling from substantially at earth orearth orbit to the moon or moon orbit in a space vehicle or rocket usinga capture transfer, comprising the steps of: (a) generating the capturetransfer by implementing a forward targeting process by varyingparameters for said method until convergence of target variables at themoon; and (b) traveling from substantially at the earth or the earthorbit to the moon or the moon orbit using the capture transfer by thespace vehicle or the rocket.
 3. A method of generating a capturetransfer for an object emanating substantially at a first heavenlyobject or first heavenly object orbit to arrive at a second heavenlyobject or second heavenly object orbit, comprising the sequential,non-sequential or sequence independent steps of: (a) entering parametersfor said method of generating the capture transfer; (b) implementing aforward targeting process by varying the parameters for convergence oftarget variables at the second heavenly object or the second heavenlyobject orbit from the first heavenly object or the first heavenly objectorbit; and (c) iterating step (b) until sufficient convergence to obtainthe capture transfer from the first heavenly object or the firstheavenly object orbit to the second heavenly object or the secondheavenly object orbit.
 4. A method according to claim 3, wherein saiditerating step (c) further comprises the step of iterating step (b)until sufficient convergence to obtain the capture transfer from thefirst heavenly object or the first heavenly object orbit to the secondheavenly object or the second heavenly object orbit via a weak stabilityboundary (WSB) orbit interposed therebetween.
 5. A method according toclaim 4, wherein said implementing step (b) further comprises the stepof generating a trajectory around the second heavenly body or the secondheavenly body orbit comprising at least a negligible maneuver of between2-20 meters per second at the WSB or the WSB orbit for at least one oftiming and positioning of at least one of a space vehicle, satellite androcket, prior to ejection therefrom.
 6. A method according to claim 3,wherein said implementing step (b) further comprises the step ofimplementing the forward targeting process by varying at least twospherical parameters for convergence of the target variables at thesecond heavenly object or the second heavenly object orbit, whilemaintaining at least one classical variable used in said forwardtargeting process substantially fixed.
 7. A method according to claim 3,wherein said implementing step (b) further comprises the step ofimplementing the forward targeting process by varying velocity magnitudeV_(E), and flight path angle γ_(E) for convergence of the targetvariables at the second heavenly object or the second heavenly objectorbit, the target variables including radial distance, r_(M), andinclination i_(M).
 8. A method according to claim 7, further comprisingthe steps of: (d) transforming converged values of V_(E), γ_(E) intoclassical elements; (e) transforming the classical elements to sphericalcoordinates, wherein the spherical coordinates include the convergedvalues of V_(E), γ_(E), and longitude α_(E), latitude δ_(E), flight pathazimuth/angle with vertical σ_(E) are changed.
 9. A method according toclaim 7, wherein the velocity magnitude V_(E), and the flight path angleγ_(E) are decoupled from the second heavenly body or the second heavenlybody orbit in the capture transfer.
 10. A method according to claim 7,wherein the velocity magnitude V_(E), and the flight path angle γ_(E)are decoupled from angular elements of the first heavenly body includinginclination i_(E), ascending node relative to earth Ω_(E), and argumentof periapsis relative to the first heavenly body ω_(E).
 11. A methodaccording to claim 3, wherein said implementing step (b) furthercomprises the step of implementing the forward targeting processcomprising a second order Newton algorithm, and wherein the second orderNewton algorithm utilizes two control variables including velocitymagnitude V_(E), and flight path angle γ_(E) that are varied to achievecapture conditions at the second heavenly body or the second heavenlybody orbit using two target variables including radial distance, r_(M),and inclination i_(E).
 12. A method according to claim 3, wherein saidimplementing step (b) further comprises the step of generating atrajectory around the second heavenly body or the second heavenly bodyorbit comprising a negligible maneuver of between 2-20 meters per secondat a weak stability boundary (WSB) or WSB orbit associated with thesecond heavenly body.
 13. A method according to claim 12, wherein theWSB or the WSB orbit is nonlinear and being substantially at a boundaryof capture and escape, thereby allowing the capture and the escape tooccur for a substantially zero or relatively small maneuver, and whereinsolar gravitational perturbations influence the first and secondtransfers.
 14. A method according to claim 12, wherein the WSB or theWSB orbit is substantially at a boundary of interaction betweengravitational fields of the first heavenly body and the second heavenlybody.
 15. A method according to claim 12, wherein as at least one of aspace vehicle, satellite and rocket moves in at least one of the WSB orthe WSB orbit, a Kepler energy of the at least one of a space vehicle,satellite and rocket is slightly negative and substantially near tozero.
 16. A method according to claim 12, wherein the at least one ofthe WSB or the WSB orbit is realizable at the predetermined arbitraryaltitude by specifying a predetermined velocity magnitude of the atleast one of a space vehicle, satellite and rocket, thereby defining apredetermined capture eccentricity.
 17. A method according to claim 3,wherein the forward targeting process is a second order Newtonalgorithm.
 18. A method according to claim, 3, wherein the firstheavenly body or the first heavenly body orbit comprises earth or earthorbit, and wherein the second heavenly body or the second heavenly bodyorbit comprises moon or moon orbit.
 19. A method of traveling by anobject emanating substantially at a first heavenly object or firstheavenly object orbit to arrive at a second heavenly object or secondheavenly object orbit using a capture transfer, comprising thesequential, non-sequential or sequence independent steps of: (a)generating the capture transfer by implementing a forward targetingprocess by varying parameters for said method until substantialconvergence of target variables at the second heavenly object or thesecond heavenly object orbit; and (b) traveling from substantially atthe first heavenly object or first heavenly object orbit to the secondheavenly object or second heavenly object orbit using the capturetransfer by the object.
 20. A spacecraft or satellite implementing amethod of traveling from substantially a first heavenly object or firstheavenly object orbit to arrive at a second heavenly object or secondheavenly object orbit using a capture transfer, wherein the capturetransfer is generated via at least one of said spacecraft, saidsatellite and a remote system, by implementing a forward targetingprocess by varying parameters for said method until substantialconvergence of target variables at the second heavenly object or thesecond heavenly object orbit; and said spacecraft or said satellitetravel from substantially at the first heavenly object or first heavenlyobject orbit to the second heavenly object or second heavenly objectorbit using the capture transfer.